Stability of Perfectly Matched Layers for Maxwell's Equations in Rectangular Solids - HAL UNIV-PARIS8 - open access Access content directly
Preprints, Working Papers, ... Year : 2023

Stability of Perfectly Matched Layers for Maxwell's Equations in Rectangular Solids

Abstract

Perfectly matched layers are an essential tool designed in the nineties for the computation of electromagnetic waves. The method replaces the Maxwell equations by a larger system, and introduce variable absorption coefficients that are nonvanishing near the boundary of the computational box. Classic absorbing conditions are imposed at the boundary. Well posedness of the resulting initial boundary value problem is proved here for the first time. The analysis proceeds by Laplace transform in time on smoothed domains. There we design boundary conditions for a non selfadjoint Helmholtz system. Estimates uniform in the smoothing are proved using carefully constructed test functions. One estimate is of energy type with less positivity than usual. A second follows Jerison-Kenig-Mitrea from elliptic problems in Lipschitz domains.
Fichier principal
Vignette du fichier
MaxwellRotSolo.pdf (484.49 Ko) Télécharger le fichier
Origin Files produced by the author(s)
licence

Dates and versions

hal-04049577 , version 1 (28-03-2023)
hal-04049577 , version 2 (23-06-2024)

Licence

Identifiers

  • HAL Id : hal-04049577 , version 1

Cite

Laurence Halpern, Jeffrey Rauch. Stability of Perfectly Matched Layers for Maxwell's Equations in Rectangular Solids. 2023. ⟨hal-04049577v1⟩
54 View
65 Download

Share

Gmail Mastodon Facebook X LinkedIn More